Asymmetric wave transmission through one dimensional lattices with cubic-quintic nonlinearity

TL;DR

This paper investigates asymmetric wave transmission in one-dimensional cubic-quintic nonlinear lattices connected to linear chains, revealing diode-like effects and the influence of nonlinear layers on wave propagation.

Contribution

It introduces an analytical approach to calculate transmission coefficients in asymmetric cubic-quintic nonlinear lattices and explores the nonlinear cooperation effects.

Findings

Higher transmission for lower wavenumber waves.

Diode-like effect enhances with more nonlinear layers.

Nonlinear cubic and quintic responses are not simply additive.

Abstract

One dimensional lattice with an on-site cubic-quintic nonlinear response described by a cubic-quintic discrete nonlinear Schr\"odinger equation is tested for asymmetric wave propagation. The lattice is connected to linear side chains. Asymmetry is introduced by breaking the mirror symmetry of the lattice with respect to the center of the nonlinear region. Three cases corresponding to dimer, trimer and quadrimer are discussed with focus on the corresponding diode-like effect. Transmission coefficients are analytically calculated for left and right moving waves via backward transfer map. The different transmission coefficients for the left and right moving waves impinging the lattice give rise to a diode-like effect which is tested for different variations in asymmetry and site dependent coefficients. We show that there is a higher transmission for incoming waves with lower wavenumbers as compared to the waves with comparatively larger wavenumbers and a diode-like effect improves by increasing the nonlinear layers. We also show that in the context of transport through such lattices, the cooperation between cubic and quintic nonlinear response is not "additive". Finally, we numerically analyse Gaussian wave packet dynamics impinging on the CQDNLS lattice for all three cases.